In most practical implementations of the Gough-
Stewart platform, the octahedral form is either taken as it
stands or is approximated. The kinematics of this particula
r
instance of the Gough-Stewart platform, commonly known as
the octahedral manipulator, has been thoughtfully studied
. It
is well-known, for example, that its forward kinematics can
be
solved by computing the roots of an octic polynomial and its
singularities have a simple geometric interpretation in te
rms
of the intersection of four planes in a single point. In this
paper, using a distance-based formulation, it is shown how t
hese
properties can be derived without relying neither on variab
le
eliminations nor trigonometric substitutions. Moreover,
thanks
to this formulation, a family of platforms kinematically eq
uiv-
alent to the octahedral manipulator is obtained. Herein, tw
o
Gough-Stewart parallel platforms are said to be kinematica
lly
equivalent if there is a one-to-one correspondence between
their squared leg lengths for the same configuration of their
moving platforms with respect to their bases. If this condit
ion
is satisfied, it can be shown that both platforms have the same
assembly modes and their singularities, in the configuratio
n
space of the moving platform, are located in the same place.